We introduce a novel framework for Federated Class Incremental Learning, called Federated Gaussian Task Embedding and Alignment (FedGTEA). FedGTEA is designed to capture task-specific knowledge and model uncertainty in a scalable and communication-efficient manner. At the client side, the Cardinality-Agnostic Task Encoder (CATE) produces Gaussian-distributed task embeddings that encode task knowledge, address statistical heterogeneity, and quantify data uncertainty. Importantly, CATE maintains a fixed parameter size regardless of the number of tasks, which ensures scalability across long task sequences. On the server side, FedGTEA utilizes the 2-Wasserstein distance to measure inter-task gaps between Gaussian embeddings. We formulate the Wasserstein loss to enforce inter-task separation. This probabilistic formulation not only enhances representation learning but also preserves task-level privacy by avoiding the direct transmission of latent embeddings, aligning with the privacy constraints in federated learning. Extensive empirical evaluations on popular datasets demonstrate that FedGTEA achieves superior classification performance and significantly mitigates forgetting, consistently outperforming strong existing baselines.

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